Janvary 11, 1895.] 



SCIENCE. 



33 



tainahk- in long ont's. Hence one of the 

 most essential conditions for the successful 

 measurement of parallaxes is that we shall 

 be able to compare the place of the near 

 body with tliat of a more distant one situ- 

 ated in the same region of the sky. In the 

 case of ^lai-s that can always be done by 

 making use of a neigliboriug star, but when 

 A'enus is near the eai-th she is also so close 

 to the sun that stars are not available, and 

 cousecjuently her i)arallax can be satisfac- 

 torily measured only when her position can 

 be accurately referred to that of the sun, or, 

 in other words, only during her transits 

 across the sun's disk. But even when the 

 two bodies to be compared are sufficiently 

 near each other, we are still embarrassed by 

 the fact that it is more difficult to measure 

 the distance between the limb of a planet 

 and a star or the limb of the sun than it Ls 

 to measure the distance between two stars, 

 and since the discovery of so many asteroids, 

 that circumstance has led to their use for 

 determinations of the solar parallax. Some 

 of these bodies api)roach within 75,230,000 

 miles of the earth's orbit, and as they look 

 precisely like stars, the increased accuracy 

 of pointing on them fully makes up for their 

 greater distance, as compared with Mars or 

 Venus. 



After the Copernican sj'stem of the world 

 and the Xewtonian theory of gravitation 

 were accepted it soon became evident that 

 trigonometrical measurements of the solar 

 parallax might be supplemented by deter- 

 minations based on the theory of gravita- 

 tion, and the first attempts in that direction 

 were made by Macliin 1729 and T. Mayer in 

 1753. T\\c measurement of the velocity of 

 light between j)oints on the earth's surface, 

 first effected by Fizeau in 1849, opened up 

 still other possibilities, and thus for deter- 

 mining the solar parallax we now have at 

 our command no less than three entirely 

 di.stinct cla.s.se.s of mcthod.s which are known 

 respectively as the trigonometrical, the gra\ - 



itatioiial and tlic photo-tachymetrical. AVe 

 have already given a summary sketch of the 

 trigonometrical methods, as applied by the 

 ancient astronomere to the dichotomy and 

 shadow cone of the moon, and by the mod- 

 erns to Venus, Mars and the asteroids, and 

 we shall next glance briefly at the gravita- 

 tional and photo-tachymetrical methods. 



♦ :;: ^ ^ i{= :^ 



The theory of probabilitj* and uniform 

 experience alike show that the limit of ac- 

 curacy attainable with any instrument is 

 soon reached : and yet we all know the 

 fascination which coutinuallj- lures us on 

 in our efforts to get better results out of the 

 familiar telescopes and circles which have 

 constituted the standard equipment of ob- 

 servatories for nearly a century. Possibly 

 these instruments may be capable of indi- 

 cating somewhat smaller quantities than 

 we have hitherto succeeded in measuring 

 with them, but their limit cannot be far off 

 because thej- already show the disturbing 

 effects of slight inequalities of temperature 

 and other uncontrollable causes. So far as 

 the.se effects are accidental they eliminate 

 themselves from every long series of obser- 

 vations, but there always remains a residuum 

 of constant error, perhaps quite unsus})ected, 

 which gives us no end of trouble. Encke's 

 value of the solar parallax affords a fine 

 illustration of this. From the transits of 

 Venus in 1761 and 1769 he found 8'58 

 seconds in 1824, which he subseciuently 

 corrected to 8*57 seconds, and for thirty 

 years that value was universally accepted. 

 Tlie fii-st objection to it came from Hansen 

 in 1854, a second followed from Le Verrier 

 in 1858, both based upon facts connected 

 with the lunar tlieory, and eventually it 

 became evident that Encke's parallax was 

 about one-(iuarter of a second too small, 

 Now please observe that Encke's value 

 was obtained trigonometrically, and its 

 inaccuracy was never suspected until it 

 was revealed by gravitational methods 



